Prove that a line that divides two sides of a triangle proportionally is parallel to the third side. Be sure to create and name
the appropriate geometric figures.
1 answer:
Answer:
Given: A triangle ABC and a line DE parallel to BC.
To prove: A line parallel to one side of a triangle divides the other two sides proportionally.
Proof: Consider ΔABC and DE be the line parallel to Bc, then from ΔABC and ΔADE, we have
∠A=∠A (Common)
∠ADE=∠ABC (Corresponding angles)
Thus, by AA similarity, ΔABC is similar to ΔADE, therefore
AB/AD= AC/AE
⇒AD+DB/AD = AE+EC/AE
⇒1+DB/AD = 1+ EC/AE
⇒DB/AD = EC/AE
Therefore, a line parallel to one side of a triangle divides the other two sides proportionally.
⇒Therefore Proved
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<h2>Therefore he took 40 gram of 
type solution and 10 gram of 
type solution.</h2>
Step-by-step explanation:
Given that , A pharmacist 13% alcohol solution another 18% alcohol solution .
Let he took x gram solution of type solution
and he took (50-x) gram of type solution.
Total amount of alcohol = gram
Total amount of solution = 50 gram
According to problem
⇔
⇔
⇔- 5x= 700 - 900
⇔5x = 200
⇔x = 40 gram
Therefore he took 40 gram of type solution and (50 -40)gram = 10 gram of
type solution.